talkConstructing triple categories of cybernetic systems

We illustrate a generalized version of the Para construction which allows to systematically construct triple categories of cybernetic processes, as well as further extensions thereof to cybernetic systems. While Para works for actions in categories, our generalization works for any suitably complete 2-category and for more general notions of action (what we call 'oplax dependent actegories'). To exemplify the construction, we show how applying our generalized Para to the self-action of a monoidal double category of lenses and charts produces a triple category of parametric lenses, lenses and charts which improves on Spivak and Shapiro's Org.